snr {bspec} R Documentation

## Compute the signal-to-noise ratio (SNR) of a signal

### Description

Compute the SNR for a given signal and noise power spectral density.

### Usage

snr(x, psd, two.sided = FALSE)


### Arguments

 x the signal waveform, a time series (ts) object. psd the noise power spectral density. May be a vector of appropriate length (length(x)/2+1) or a function of frequency. two.sided a logical flag indicating whether the psd argument is to be interpreted as a one-sided or a two-sided spectrum.

### Details

For a signal s(t), the complex-valued discrete Fourier transform \tilde{s}(f) is computed along the Fourier frequencies f_j=\frac{j}{N \Delta_t} | j=0,\ldots,N/2+1, where N is the sample size, and \Delta_t is the sampling interval. The SNR, as a measure of "signal strength" relative to the noise, then is given by

\varrho=\sqrt{\sum_{j=0}^{N/2+1}\frac{\bigl|\tilde{s(f_j)}\bigr|^2}{\frac{N}{4\Delta_t} S_1(f_j)}},

where S_1(f) is the noise's one-sided power spectral density. For more on its interpretation, see e.g. Sec. II.C.4 in the reference below.

### Value

The SNR \varrho.

### Author(s)

Christian Roever, christian.roever@med.uni-goettingen.de

### References

Roever, C. A Student-t based filter for robust signal detection. Physical Review D, 84(12):122004, 2011. doi: 10.1103/PhysRevD.84.122004. See also arXiv preprint 1109.0442.

matchedfilter, studenttfilter

### Examples

# sample size and sampling resolution:
N       <- 1000
deltaT  <- 0.001

# For the coloured noise, use some AR(1) process;
# AR noise process parameters:
sigmaAR <- 1.0
phiAR   <- 0.9

# generate non-white noise
# (autoregressive AR(1) low-frequency noise):
noiseSample <- rnorm(10*N)
for (i in 2:length(noiseSample))
noiseSample[i] <- phiAR*noiseSample[i-1] + noiseSample[i]
noiseSample <- ts(noiseSample, deltat=deltaT)

# estimate the noise spectrum:
PSDestimate <- welchPSD(noiseSample, seglength=1,
windowingPsdCorrection=FALSE)

# generate a (sine-Gaussian) signal:
t0    <- 0.6
phase <- 1.0
t <- ts((0:(N-1))*deltaT, deltat=deltaT, start=0)
signal <- exp(-(t-t0)^2/(2*0.01^2)) * sin(2*pi*150*(t-t0)+phase)
plot(signal)

# compute the signal's SNR:
snr(signal, psd=PSDestimate\$power)


[Package bspec version 1.6 Index]